Abstract

Grand Unified Theories (GUTs) offer an attractive framework for flavour models, since they feature relations between quarks and leptons. Combining them with Supersymmetry (SUSY) and flavour symmetries, we derive predictions for the flavour and SUSY flavour structure from various GUT models and discuss how the double missing partner mechanism (DMPM) solution to the doublet-triplet splitting problem can be combined with predictions for GUT scale quark-lepton Yukawa coupling relations. We construct two predictive SUSY SU(5) GUT models with an A4 flavour symmetry, that feature realistic quark-lepton Yukawa coupling ratios and mixing angle relations. These GUT scale predictions arise after GUT symmetry breaking from a novel combination of group theoretical Clebsch-Gordan factors, and we carefully construct additional shaping symmetries and renormalisable messenger sectors to protect the models' predictions from dangerous corrections. The major difference between both models are their respective predictions of a normal and inverse neutrino mass ordering. We perform Markov Chain Monte Carlo analyses, fit to experimental data, and discuss how the models can be tested by present and future experiments. To combine predictive GUT scale quark-lepton Yukawa coupling ratios with the DMPM in SUSY SU(5), we introduce a second GUT breaking Higgs field in the adjoint representation. Two explicit flavour models with different predictions for the GUT scale Yukawa sector are presented, including shaping symmetries and renormalisable messenger sectors, and combined with the DMPM. We calculate the effective masses of the colour triplets mediating proton decay and find that they can be made sufficiently heavy. In SUSY theories, the one-loop SUSY threshold corrections are of particular importance in investigating GUT scale quark-lepton mass relations and thus link a given GUT flavour model to the sparticle spectrum. We calculate the one-loop SUSY threshold corrections of the full MSSM Yukawa coupling matrices in the electroweak-unbroken phase and introduce a new software tool SusyTC as a major extension to the Mathematica package REAP. Finally we find predictions for the CMSSM parameters and sparticle masses from the GUT scale Yukawa coupling ratios used in the flavour models of this thesis.